Hours after a Conservative chancellor shackled the state with the toughest budget in recent memory, the hoisting of a Cuban flag above one of London's most affluent areas smacked of token defiance.

In fact, the flag-raising is an annual event. Figures in the labour movement had gathered at Clapham Common for a display of solidarity with the communist outpost, but their most pressing concerns were closer to home: how to knock George Osborne off course from a two-year public sector pay freeze, pension changes and 25% cuts at most government departments.

Of all the attendees, Len McCluskey carries the greatest promise of disrupting the Tories' fiscal agenda, through the 1.6 million members he represents. The assistant general secretary of Britain's largest trade union, Unite, has played a prominent role in the British Airways cabin crew dispute and foresees a wave of industrial confrontations as the cuts bite. As one of the favourites in this year's election for the job of Unite's general secretary, McCluskey could inherit a responsibility that will put his organisation on a collision course with public opinion.

Holding forth to an audience of hundreds in the setting of Maritime House – an imposing edifice owned by the RMT railworkers' union, symbolising a time when unions had more serious heft in Britain's political and economic life – McCluskey sounds like he is on the campaign trail: "Solidarity, comrades, is what we are about. It runs through our veins. It is what makes us different to the bosses' class and the elite who rule us and try to dominate us."

Continuing this theme in a nearby pub, the 59-year-old Liverpudlian sees parallels with a time when unions had greater power. A trade union official for more than three decades, McCluskey became an officer for Unite's predecessor, the Transport and General Workers' Union, in 1979 after more than 10 years' employment as a draughtsman in the Liverpool docks. In the mid-1980s his union was part of a "united front" against a government squeeze on the city's finances that included Derek Hatton, Liverpool council's then deputy leader. Along with the miners' strike, it was one of the era's defining clashes with the Tory government.

Common cause

McCluskey believes his role now, as then, is to persuade Unite's more than a million-strong private sector members that they have common cause with Unite's 250,000 public sector membership – dinner ladies, teaching assistants, hospital porters – who face the biggest threat from Osborne's cuts.

He recalls:"I was stood down from my industrial work [at the Ford engineering plant in the 1980s] to co-operate with the local council and the private sector membership, to make them understand that the attacks on the city council were going to affect them too."

Appropriately, the TV in the corner is showing Greece's football team struggling in a World Cup match that looks every bit as lost as the country's fight with a €300bn debt.

"I don't want to get too hyped up about David Cameron being Margaret Thatcher mark II," McCluskey says. "We've moved on but we mustn't make the same mistakes again. If workers have confidence, then my experience tells me that anything is possible. Look at what happened with Thatcher and the poll tax. It was people power that brought down a person who seemed impregnable."

Freezing public sector pay and cutting jobs will undermine the economic recovery, he says. So what does Unite propose instead? "The first way to solve any debt crisis is economic growth." Introducing the Tobin tax on financial transactions and clamping down on tax evasion by companies and the rich will claw back up to £25bn a year. "We'd have the money to pay off the debt, increase public services and public sector pay, but most importantly to invest in our manufacturing base."

Inevitably, the conversation turns to the industrial action that could arise from spending cuts. "We need to create an alliance of resistance because our members don't want pay freezes, pay cuts and a tax on their services and communities. The unions have to be responsible for co-ordinating that action."

Does that include strikes? "Absolutely. They talk about public sector workers as if they're devils. We're talking about people who teach our children, treat the sick, clean our streets, people who are responsible for building the fabric of the communities in which we live. We need to tell our private sector workers that this is their fight too.

"It's an old trick of divide and rule. They try to break private sector workers away from public sector workers. That's a horrible, insidious strategy and we have to counter it by explaining to private sector workers that cuts to public sector spending will affect their lives."

Trade union membership in the UK is now at 7.6 million, down from 13.2 million at its peak in 1979, but about a fifth of the working-age population nonetheless. McCluskey adds: "I believe trade unions do need to come together in order to determine strategies. If our members need to take industrial action, then we have to hit the streets and say we are not prepared to accept this."

Contrary to how his words read, McCluskey is not standing on the table at this point. As with his public appearances during the BA dispute, his Merseyside lilt is less strident than that of the man he hopes to succeed at the head of Unite, the union's joint general secretary Tony Woodley.

Not that his more conciliatory tone has produced a breakthrough in the worst industrial row in the airline's history. After 22 days of strikes by flight attendants, Unite – which represents three-quarters of BA's 38,000-strong workforce – is preparing to hold another ballot of 11,000 cabin crew over BA's use of auxiliary crew and the withdrawal of travel perks from strikers.

Unite has offered to suspend strike action if BA fully reinstates staff travel, but the airline is standing firm and has pledged to run 100% of its Heathrow long-haul service if there is another walkout, rostered for August. Under that scenario, the power of Unite could be severely blunted within BA.

McCluskey rejects warnings that the union in effect faces a lock-out at BA. "The truth is, BA cannot win this dispute because they cannot carry the workforce with them. They will never be able to project the image that made BA the world's premier airline."

A senior pilot concurs, describing working conditions as "unsustainable" because staff on flights are so wary of each other – about 70 crew have been suspended during the dispute.

BA denies Unite's claims that it is attempting to break trade unionism within the airline but McCluskey feels that an eight-week spell leading negotiations this year was a waste of time. "All they were doing was buying time to build up their scab workforce."

BA denies this strongly, having trooped through the doors of the conciliation service, Acas, and the TUC many times this year.

McCluskey tries to play down the wider significance of a dispute between Britain's largest private sector union and one of the UK's most famous corporate names. "BA is a normal industrial dispute." He adds: "I think the media are hyping this up. To me it is another dispute that has to be settled."

With that, he returns to his comrades at Maritime House, well aware that a union-wide confrontation with the government will need no exaggeration.